Problem: Multiply the following complex numbers: $({2}) \cdot ({1})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2}) \cdot ({1}) = $ $ ({2} \cdot {1}) + ({2} \cdot {0}i) + ({0}i \cdot {1}) + ({0}i \cdot {0}i) $ Then simplify the terms: $ (2) + (0i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 2 + (0 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 2 + (0 + 0)i - 0 $ The result is simplified: $ (2 - 0) + (0i) = 2 $